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Simplifying (27x2) + -1x + -156 = 0 Reorder the terms: -156 + -1x + (27x2) = 0 Solving -156 + -1x + (27x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -5.777777778 + -0.03703703704x + x2 = 0 Move the constant term to the right: Add '5.777777778' to each side of the equation. -5.777777778 + -0.03703703704x + 5.777777778 + x2 = 0 + 5.777777778 Reorder the terms: -5.777777778 + 5.777777778 + -0.03703703704x + x2 = 0 + 5.777777778 Combine like terms: -5.777777778 + 5.777777778 = 0.000000000 0.000000000 + -0.03703703704x + x2 = 0 + 5.777777778 -0.03703703704x + x2 = 0 + 5.777777778 Combine like terms: 0 + 5.777777778 = 5.777777778 -0.03703703704x + x2 = 5.777777778 The x term is -0.03703703704x. Take half its coefficient (-0.01851851852). Square it (0.0003429355282) and add it to both sides. Add '0.0003429355282' to each side of the equation. -0.03703703704x + 0.0003429355282 + x2 = 5.777777778 + 0.0003429355282 Reorder the terms: 0.0003429355282 + -0.03703703704x + x2 = 5.777777778 + 0.0003429355282 Combine like terms: 5.777777778 + 0.0003429355282 = 5.7781207135282 0.0003429355282 + -0.03703703704x + x2 = 5.7781207135282 Factor a perfect square on the left side: ((x) + -0.01851851852)((x) + -0.01851851852) = 5.7781207135282 Calculate the square root of the right side: 2.403772184 Break this problem into two subproblems by setting ((x) + -0.01851851852) equal to 2.403772184 and -2.403772184.Subproblem 1
(x) + -0.01851851852 = 2.403772184 Simplifying (x) + -0.01851851852 = 2.403772184 x + -0.01851851852 = 2.403772184 Reorder the terms: -0.01851851852 + x = 2.403772184 Solving -0.01851851852 + x = 2.403772184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01851851852' to each side of the equation. -0.01851851852 + 0.01851851852 + x = 2.403772184 + 0.01851851852 Combine like terms: -0.01851851852 + 0.01851851852 = 0.00000000000 0.00000000000 + x = 2.403772184 + 0.01851851852 x = 2.403772184 + 0.01851851852 Combine like terms: 2.403772184 + 0.01851851852 = 2.42229070252 x = 2.42229070252 Simplifying x = 2.42229070252Subproblem 2
(x) + -0.01851851852 = -2.403772184 Simplifying (x) + -0.01851851852 = -2.403772184 x + -0.01851851852 = -2.403772184 Reorder the terms: -0.01851851852 + x = -2.403772184 Solving -0.01851851852 + x = -2.403772184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01851851852' to each side of the equation. -0.01851851852 + 0.01851851852 + x = -2.403772184 + 0.01851851852 Combine like terms: -0.01851851852 + 0.01851851852 = 0.00000000000 0.00000000000 + x = -2.403772184 + 0.01851851852 x = -2.403772184 + 0.01851851852 Combine like terms: -2.403772184 + 0.01851851852 = -2.38525366548 x = -2.38525366548 Simplifying x = -2.38525366548Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.42229070252, -2.38525366548}
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